Does your school happen to have an aferschool program that is not technically considered "day care"?
Plano has the PASAR program which is before and after school. After school, all children grades k-5 (at our particular elementary) go to the gym when class is over. While other children are waiting on carpool, day care, buses, walking, etc... the PASAR children are checked in and given a snack.
After all the carpool, buses, etc clears out.. then the group is divided. About 1/2 go outside for outdoor running, etc... "recess" and the other 1/2 are divided are go to particular teacher's rooms for tutoring, get homework done for the night, etc. About 1/2 way though the PASAR timeframe, they switch and the other group goes outside while the first group does homework, etc. My understanding is that it isn't that expensive. Parents have until 6pm to pick children up and they can be dropped off by 7am for breakfast and before school.
That said.... the apt is less than 1/2 mile, you have a 10 yr old who is ready for some independence and responsibility. I think your decision is not a right or wrong one... it depends on the maturity of your 10 yr old and what he can handle. Is he responsible to go in lock the door, do homework, etc.
Maybe you can let him try this in baby steps so he can show you how responsible he is. Many children this age long for independence and as moms, it is hard to let go, although we have to at some point.
Also, if you allow this, make sure he has a phone so he can check in.
Our daughter never walked to/from school.. she drives now and my rule is STILL text me to let me know you are at school ok. Her drive is about 20 minutes and she'll be a Sr next year. I don't have to remind her to check in.. she has always been good about letting me know she arrived safely.
Best wishes to you!!